Binomial trees might be great in the classroom, but in the real world they’re so much firewood writes This e-mail address is being protected from spambots. You need JavaScript enabled to view it of MathConsult

 I don’t like trees. At least I don’t like them when used for the numerical solution of partial differential equations. From the theoretical point of view, binomial trees are quite appealing in teaching the concept of noarbitrage.

Nevertheless, from the numerical point of view, there are major drawbacks: You typically need a huge number of time steps to obtain a reasonable accuracy by binomial trees. This could be improved by trinomial trees, but the problem of instability remains.

To be more specific: Trinomial trees are explicit numerical schemes for typically parabolic differential equations, which may lead to severe stability problems. In the case of mean-reverting models, this is well known. Fiddling
around with the branching of the tree makes the method stable again, but changes the domain of the partial differential equation and therefore its solution.

This article should give an overview how we at MathConsult work on taking the tree risk out of computational finance.

Linz is the industrial center of Austria and also one of the largest centers for industrial and applied mathematics on the worldwide scale.

To get the whole article, please download the article How to kill your trees properly